Search

The purpose of this resource is to help math teachers unpack, understand, and implement the current math content and practice standards. This resource describes the progressions of learning within each course and provides content support, which includes broad ideas about effective instruction as well as practical instructional strategies. Math teachers, coaches, and leaders are encouraged to use these materials collaboratively to support ongoing instruction and the growth of individual teaching practice. The content is organized by the following domains in Geometry, including: (1) Standards for Mathematical Practice; (2) Geometry: Logic and Proofs; (3) Geometry: Points, Lines, and Angles; (4) Geometry: Transformations; (5) Geometry: Triangles; (6) Geometry: Quadrilaterals and Other Polygons; (7) Geometry: Circles; and (8) Geometry: Three-Dimensional Figures.

Mastering algebra is important for future math and postsecondary success. Educators will find practical recommendations for how to improve algebra instruction in the What Works Clearinghouse (WWC) practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students". The methods and examples included in the guide focus on helping students analyze solved problems, recognize structure, and utilize alternative approaches to solving algebra problems. Each recommendation includes the level of supporting research evidence behind it, examples to use in class, and solutions to potential implementation roadblocks. Teachers can implement these strategies in conjunction with existing standards or curricula. In addition, these strategies can be utilized for all students learning algebra in grades 6-12 and in diverse contexts, including during both formative and summative assessment. Administrators and professional development providers can use the guide to implement evidence-based instruction and align instruction with state standards or to prompt teacher discussion in professional learning communities. Appended are: (1) Postscript from the Institute of Education Sciences; (2) About the Authors; (3) Disclosure of Potential Conflicts of Interest; and (4) Rationale for Evidence Ratings. A Glossary is included.

The No Child Left Behind Act of 2001 has increased the role of assessment in K-12 education. Designed to ensure that all students meet high academic standards, the law currently requires states receiving Title I funds to test all children annually in reading and math in grades 3 through 8 and report student performance disaggregated by poverty, race and ethnicity, disability, and limited English proficiency. By the 2005-06 school year, tests must be expanded to include at least one year between grades 10-12, and by 2007-08, states must also include science assessments at least once in grades 3-5, grades 6-9, and grades 10-12. The law requires states to set annual measurable objectives to track student progress towards reaching proficiency, with the ultimate goal that "all groups of students--including low-income students, students from major racial and ethnic groups, students with disabilities, and students with limited English proficiency--reach proficiency within 12 years". This report summarizes the spring 2003, fourth-grade reading achievement data from 29 different schools in an urban school district in the Pacific Northwest. The original data set contained 1,290 students, but some students were missing data in some but not all of the dependent variable measures, so the total sample size used for different analyses varies by measure. Item Analysis for District Reading Test, Selected Response: Forms A and B is appended. (Contains 17 tables.)

The National Assessment of Educational Progress (NAEP) collects data in the form of repeated, discrete measures (test items) with hierarchical structure for both measures and subjects, that is complex by any standard. This complexity has been managed through a "divide and conquer" approach of isolating and evaluating sources of variability one at a time, using a sequence of relatively simple analyses. The cost of this simplicity for the NAEP has been limits on the propagation of information from one subanalysis to another. This has made some questions that would be relatively straightforward to address in ordinary circumstances, quite difficult to answer for the NAEP. This study considers NAEP's fragmented analysis of errors in the rating of open-ended responses, develops methodology for more unified analyses, and applies the methodology to the analysis of rater effects in NAEP data. How to minimize rater effects using modern imaging technology is studied, and conclusions and recommendations are drawn in light of these analyses. (Contains 15 figures, 13 tables, and 30 references.) (SLD)

A discussion of cognates in second language teaching, particularly in English as a Second Language (ESL), looks at reasons and methods for teaching both true and false cognates ("friends"). A definition of cognates is offered, and a distinction is made between a cognate and a borrowed word, with examples from several languages. Textbooks' treatment of cognates is examined, and some problems arising from overemphasis on use of true cognates are noted, including potential for stilted language use and the danger of adopting false cognates. It is recommended that the teaching of false cognates be included in ESL instruction, to promote vocabulary development. Techniques include the teacher's development and incorporation into instruction of a collection of false cognates, using standard language exercises and games for identifying false cognates. Examples are offered. Contains six references. (MSE)

This guide to ERRATA, a set of HyperCard-based tools for response analysis and error diagnosis in language testing, is intended as a user manual and general reference and designed to be used with the software (not included here). It has three parts. The first is a brief survey of computational techniques available for dealing with student test responses, including: editing markup that identifies spelling, capitalization, and accent errors and extra, missing, or out-of-order words; pattern matching for rapid identification of specific grammatical errors, keyword searches, and easy specification of alternate answers; and error-tolerant parsing, which puts error diagnosis under control of a grammar and dictionary of the target language. The second section is a user's manual and tutorial guide, describing ERRATA and offering examples of its use. Section three is a reference manual useful to anyone with unusual analysis requirements or wanting to tailor-make responses analyses. Installation and technical information is also included, and complete program code is appended. (MSE)

A discussion of English-as-a-Second-Language (ESL) teaching focuses on the relationship of lexical items to the syntactic situations in which they may occur, and the importance of teaching this relationship to language learners. First, common errors made by ESL students that are attributable to lack of syntactic context knowledge are identified. Included are these error types: verb + preposition, adjective + preposition, noun + preposition; transitive vs. intransitive verbs; direct objects; causatives; verb + complement(s); and connectors. Then the usefulness of some specific current ESL reference books and texts to inform teachers and students of this aspect of lexicon is discussed. These include dictionaries, handbooks of usage, and textbooks. Finally, ways in which the classroom teacher can present this important but difficult-to-generalize information are examined, using specific situations and possible alternative classroom treatments. A number of overhead masters used in presentation of the paper are included, and the handout offered is appended. (MSE)

Considers the existence of halo effects in individuals' evaluations of target communicators across different dimensions. Notes that halo effects result from raters' inability to discriminate among conceptually distinct and theoretically independent aspects of a target's behavior. Discusses current conceptions of halo error and suggests several potential sources of halo error. (SG)

Research into process-oriented writing instruction for native speakers of English can improve instruction in writing for students of English as a second language (ESL). Process-oriented instruction focuses on the processes of writing rather than on the finished product. A comparison of writing samples of native speakers from remedial courses and ESL students shows that despite differences in the types of grammatical and syntactical errors made, significant similarities exist. The ESL writer and remedial writer both approach writing in a linear fashion with preconceived ideas, and arrive at a conclusion too soon and without sufficient illustration or detail. Prewriting exercises in internal conversation are important for ESL students to develop rhetorical skills. In addition, instruction in two major native speaker composition skills, freewriting and problem-solving, are applicable to ESL writing instruction. Freewriting is a technique for exploring and synthesizing original ideas, helping to break down inhibitions about expressing ideas by deemphasizing correctness of surface structures. The problem-solving technique approaches a writing task as a problem to be solved, considering desired outcome, intended audience, and potential problems, much like notional-functional considerations identifying content and purpose. Each technique may have specific application to cultural groups. Additional classroom practices include using real communicative situations, sentence-combining exercises, teacher writing samples, and active revision. (MSE)

Presented are training materials for use in a teachers' workshop--providing methods for teaching essential skills to students with learning difficulties and planning individual instructional sequences as students' skill needs change. Included are the following ten modules: (1) defining the problem and identifying what will meet the student's needs, (2) task analysis, (3) error pattern analysis, (4) systematic inquiry, (5) discovering what Sally can and can't do and setting priorities, (6) behavioral objectives, (7) learning methods, (8) task analysis of materials, (9) matching learner characteristics with material characteristics, and (10) designing materials for the educationally handicapped. Each module contains three sections titled "Facilitator Notes", "Activity Notes", and"Activity Sheets"; and some contain sections for worksheets, recording sheets, activities completed by other participants, demonstrations and articles. Appended are notes on the module tests and the global test given to participants; the tests and answer keys; additional evaluation procedures; and bibliographies of articles, books, and tests. (IM)

The purpose of this paper is to clarify the theoretical concept of a syllabus by specifying important variables and priorities in its preparation and application. The scope and nature of the syllabus are discussed, followed by an examination of learning processes and strategies. The focus of the syllabus is seen as being fluency and flexibility, and as possible having some effect on student motivation. Since learning must be seen from the student's point of view, learning-focused materials are considered necessary in the syllabus. Some practical considerations are discussed, specifically general criteria for the language syllabus, sequencing, and item entry. Results of a questionnaire are shown, in which 50 ESL teachers indicated at what point they would introduce each of 45 grammatical structures. These results are compared to responses given by non-ESL educators. The use of Learning Effort Units (LEU's) as criteria for the entry of structures in a syllabus are discussed. It is hoped that this study will demonstrate the utility of an independent, objective teacher consensus in preparing a syllabus based on sound linguistic applications and not necessarily mirrored in existing language learning materials. (Author/AM)

This monograph provides an overview of computer-based assessment and error analysis in the instruction of elementary students with complex medical, learning, and/or behavioral problems. Information on generating and scoring tests using the microcomputer is offered, as are ideas for using computers in the analysis of mathematical strategies and errors of students. Examples of specific computer applications are included. Issues such as interactive assessment, curriculum-based assessment, and artificial intelligence are also considered. The systems save examiner time, reduce scoring errors, and provide teachers with information that would otherwise be difficult to obtain. More advanced systems will be able to guide the teacher through the necessary steps for the analysis of learning problems, test the student directly where appropriate, analyze student performance data, and prescribe appropriate instructional strategies. A glossary of terms concludes the monograph. (Contains 20 references.) (DB)

Causes of language fossilization and ways to overcome it are considered. Fossilization is the relatively permanent incorporation of incorrect linguistic forms into a person's second language competence. The discussion is focused on fossilization of incorrect syntactical rules, based on experiences with learners of English as a second language at the University of Maryland, Baltimore County. Students who have been in the United States for years often demonstrate fossilization. While they can communicate basic needs and some may communicate at complex levels, the students have developed their own personal, idiosyncratic interlanguages, which are simplified versions of English. The causes are lack of formal instruction and insufficient corrective feedback from native speakers and classroom teachers. It is suggested that helping students overcome fossilized items requires positive affective feedback but negative cognitive feedback when fossilized structures are used. A problem for educators is to convince the students that they need remedial assistance without intimidating or antagonizing them. Placement essays and grammar tests can be used to determine whether students need a remedial course or can proceed to an English as a second language composition course. In the remedial class, the span in levels of proficiency causes problems. Tutorial help for less proficient students and extra language lab work, as well as individualized instruction, are possible solutions. The remedial class includes formal grammar instruction, oral exercises with corrective feedback, substitution and sentence manipulation drills, written exercises, short composition assignments, and dictations in class. (SW)

In early computer assisted instruction (CAI), negative feedback often insulted students and/or provided no useful knowledge. In classroom settings, teachers use the following approaches in dealing with students' wrong answers: (1) ask the question again, louder and slower; (2) ask the question again, using different words; (3) back up and reteach the past three minutes/hours/days; and (4) keep still, listen to the students and let their behavior reveal where the source of the misunderstanding lies. The latter approach suggests that students answer correctly or incorrectly for a reason and that observation of their behavior can indicate ways to help them correct their misunderstandings. For example, using algorithms to describe student behavior can help minimize student errors in learning a procedure. Designing CAI materials for procedural learning should include two steps: construction of the correct production system or algorithm and construction of potential "buggy" or incorrect procedures, followed by incorporation of instructional error checking into the program. This paper concludes with the description of an interactive video program developed to teach procedures for diagnosing reading problems which included three incorrect algorithms. Responses to students' choice of incorrect algorithms were positively phrased and offered hints. Responses for correct answers explained why the answer was correct. Three references are listed. (LMM)

Some possible reasons why remediation is needed in mathematics instruction are presented. The need to diagnose the problem and then provide appropriate, effective remediation is discussed. Four guiding principles for diagnosis are presented, followed by six questions covering hypotheses about the source of the difficulty. Suggestions are then given for remedial work on errors with basic facts and on computational procedures. The game of "Multivision" is included. Finally, grouping for remediation is discussed. (MNS)

The nature and extent of misreporting by applicants for the Basic Educational Opportunity Grant program was investigated. Types of potential program abuse were assessed, along with the accuracy of income estimates that students make on Supplemental Basic Grant applications, which are the basis for determining a student's eligibility. Attention was directed to: characteristics of a sample of 2,479 students using the Supplemental Basic Grant application in 1975-1976, types of changes made to applicants' Student Eligibility Reports between the regular and supplemental applications submitted in 1975-1976, and the kinds of applications the sample filed in 1974-1975 and 1976-1977. The supplemental application recognizes that students' previous year financial resources are not always a valid basis for predicting current financial strength and determining eligibility. Findings of the report include: applicants made failry accurate estimates of their 1975 adjusted gross income; 58 percent of the sample were dependent and 42 percent were independent students; the predominant reasons for filing 1975-1976 supplemental applications related to unemployment of the student, parent, or spouse; and less than one-fourth filed a 1974-1975 application, while almost two-thirds filed a 1976-1977 application. (SW)

The validity of information provided in applications to the Basic Educational Opportunity Grant (BEOG) program was studied, along with procedures used in recovering overpayments. The objective was to investigate misreporting and misuse of the BEOG program. A 1977-1978 study reviewed cases referred to the U.S. Office of Education by educational institutions. Attention was directed to reasons for institution referrals, the mode of case resolution, the impact of the validation process on Student Eligibility Indices, the impact on changes to individual Student Eligibility Reports (SERs) entries, and types of documentation used to support case referrals. Another study investigated a random sample of about 8,000 applicants who were selected based on 1977-1978 applications that were believed to entail errors on SERs. The criteria identified cases in which internal inconsistencies were apparent in the application. In addition, a separate set of criteria for identification of potential misreporters was developed: American College Testing Program criteria that accounted for possible sources of error that had been identified through past validation efforts and studies. The outcomes of the first year of operation of the Overpayment Recovery System were also assessed. Statistical findings of the studies are included in approximately 50 tables. (SW)

The issues, options, and procedures for annually measuring overall payment error in the Pell Grant program are specified in detail. Guidelines for establishing a definition of Pell Grant payment error are provided, and the design issues related to error measurement are examined. A comparison is made of options for selecting a study sample and for collecting data required to measure payment error. Data collection procedures are specified in detail, along with procedures needed to create a study database from the collected data. Guidelines for data analysis are also included. The correct award to students is based on such factors as enrollment status and student costs. Error measurement in the Pell program involves time-related research design factors, all of which must be understood when planning the data collection effort and when analyzing the data. Data collection activities are outlined for sample selection, student/parent interviewing, collecting hardcopy secondary data, and collecting data from institutions. Tasks and procedures required to create the database include: receipt of data, editing and coding, data entry, machine edit and updating, reformatting files for analysis package, producing marginal tabulations, merging data files, and reviewing case for quality control. Appended are: a glossary; a description of measurement tolerances of error in the program; algebraic specifications of error measures; and an estimate of requirements for conducting an assessment of overall payment error in the Pell Grant program. (SW)

The development of a number of error-prone models to select Pell Grant recipients for validation is discussed. The 1983-1984 Pell Grant validation strategy consists of a two-stage approach: selection using Pre-Established Criteria (PEC) followed by selection using Error Prone Modeling (EPM). The database used for model development consists of a sample of 1980-1981 Pell Grant Recipients. The policy question is which students should be selected for various types of validation measures. Eight effectiveness measures are defined, and for each measure an error-prone model is developed that will identify those cases for which the corresponding type of validations will uncover the highest level of error. The data elements include: income, U.S. taxes paid, household size, nontaxable income, liquid assets, spouse income, and dependency status. The eight models are then compared in order to identify the most cost-effective approach to marginal selection for validation. The measures refer only to the payment consequences of discrepancies likely to be uncovered by the corresponding type of validation being used. Detailed appendices include EPM error tables and Automatic Interaction Detector coding categories for predictor variables. (SW)

The development of the error prone model (EPM) for the 1984-1985 student financial aid validation criteria for Pell Grant recipient selection is discussed, based on a comparison of the 1983-1984 EPM criteria and a newly estimated EPM. Procedures/assumptions on which the new EPM was based include: a sample of 1982-1983 Pell Grant recipients originally selected for the Pell Grant Quality Control Study was used for estimation; cases assumed to have met the Pre-Established Criteria were excluded from the estimation database; and the model was based on an exploratory data analysis approach embedded in the Automatic Interaction Detector (AID) software package. To develop the new EPM, error was defined as the potential change in the Student Aid Index resulting from validation on four application items: household size, U.S. taxes, and adjusted gross income of dependent parents or independent students, and student/spouse net income for dependent students. The 41 applications items that were considered as possible variables for predicting errors are identified. Information is also provided on the 18 final groups that emerged from the AID sequential search estimating procedure. Appended are descriptions of the 28 validation criteria for 1984-1985. (SW)

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example of the error. Major concept headings include the following: (1) Basic Problem Solving Skills; (2) Averages; (3) Whole Numbers; (4) Fractions; (5) Decimals; (6) Percents; (7) Integers; (8) Exponents; (9) Simple Equations; (10) Ratios and Proportions; (11) Geometry; and (12) Graphing. (RH)

Structuring the algebra course to provide a link between a student's existing knowledge and the new topic being presented is discussed. Developing relationships among topics is suggested through examples describing a mathematical problem and effective teaching approaches. Stress is placed on teachers reflecting on mistakes pupils are likely to make with particular content and recalling relevant previously learned material. (MNS)

Students make errors in mathematics for a variety of reasons. It is the job of the educator to identify the source of these errors and to assist students in correcting them. The purpose of this monograph is to help identify, analyze, and evaluate students' computational proficiency. This monograph is divided into four sections: "Whole Numbers"; "Fractions"; "Decimals"; and "Percents." Each section is arranged according to specific computational skills. Each computational skill is examined via the following components: (1) skill (giving the specific computational skill to be examined; (2) example (offering a sample problem that could lead to typical student errors); (3) entry conditions (listing the mathematical prerequisites for mastery of the skill being examined); (4) correct solution (showing correct answer to the given sample); (5) errors, identification and analysis (highlighting typical student errors and analyzing their possible source); and (6) practice (providing problems similar in scope to the example). (YP)

Students of English as a second language (ESL) often come to the classroom with little or no experience in writing in any language and with inaccurate assumptions about writing. Rather than correct these assumptions, teachers often seem to unwittingly reinforce them, actually inducing errors into their students' work. Teacher-induced errors occur when teachers mislead students by overemphasizing some aspect of the writing process or when students oversimplify and apply a principle or strategy too broadly. Two related pieces of advice commonly given to students are to use a variety of sentence structures and to avoid an unpleasant repetition of a word or phrase. Students often misunderstand these to mean: don't use the same sentence structure twice, and don't repeat a word or phrase. In response to these recommendations, students force errors into their writing, complicating it unnecessarily, making it awkward, and losing coherence. Students should first be encouraged to write coherent and error-free prose that reads smoothly, uses economical language, does not require the reader to backtrack, and allows the reader to accurately guess what the writer is saying. When taught this way, students will naturally vary their sentences and not be preoccupied unnecessarily. (MSE)

Present composition teaching and testing techniques do not formally capture student improvement across essays. Contract learning, a procedure in which student essays are error-analyzed for repeated mistakes, can do so. Correction of those repetitions becomes a set of goals on a written contract signed by the teacher and student, and the student works to accomplish the goals by the end of the term. Contract fulfillment may involve either remediation or self-motivation. Fulfillment is based on a slowing, stoppage, or reversal of error trends by the term's end. Contract results provide a new, individualized, criterion-referenced source of measurement information to be integrated with other criterion-referenced (task based) and norm-referenced (rank based) sources in an advancement decision using multiple references. Examples are given of this technique, based on 2 years of experience with the contract learning procedure. (Author/MSE)

Problems with finance data reported through the Higher Education General Information Survey (HEGIS) are reported. Less than one percent of institutions appear to have reported incorrect data for the fiscal year (FY) 1983 finance survey. One reporting problem concerns state appropriations that are radically different in previous years or that are reported as $0. For public colleges, a $0 state appropriation is a flag for a potential problem. Another flag occurs when the amount of the Pell Grants exceeds the amount of restricted federal grants and contracts, since the latter includes Pell Grants. A chart of potential errors in reporting on the FY 1983 Finance Survey indicates the name of the college, the state, the amount of potential error (state and local appropriations, government grants and contracts, total revenue, and other), and comments about each potential error. A second chart of Pell Grant reporting errors shows for each college the amount of restricted federal government grants and contracts, and the amount of Pell grants. To determine if data problems exist with the HEGIS reporting, finance data for 5 years are listed according to specific categories. (SW)

The second in a series of manuals on adults with learning disabilities, the booklet covers assessment techniques. The nature of assessment as an ongoing process is stressed, and the role of observation (both systematic and nonsystematic) and interview data are discussed. A seven-step evaluation sequence is proposed, with the major goal of interpreting the error patterns which will indicate processing strengths and weaknesses. The importance of the interview between adult education teacher and adult student is pointed out, and guidelines are suggested for structuring the interview environment. The contribution of adult education teachers to evaluation of cognitive functioning is noted. Specific measures for assessing general cognitive ability, language, academic achievement, written expression, and personality are listed. Two bibliographies are appended--one on neurological assessments, screening and placement, and prevailing assessment strategies; and one on general background information for adult education teachers encountering a learning disabled student. (CL)

This monograph provides an historical overview of handwriting assessment, followed by suggestions for informally assessing student handwriting errors and implementing improvement strategies. The monograph specifically addresses: (1) research on handwriting; (2) a rationale for remediation of handwriting errors; (3) techniques for evaluating handwriting, including qualitative and quantitative approaches; (4) purposes of instructional assessment; (5) error analysis techniques, including methods for integrating error correction into daily instruction. A case study is presented of a fifth-grade student with illegible handwriting. The student and teacher together identified illegible or nearly illegible words, determined what made the words difficult to read, identified overall problems, prioritized the problems, established contingencies for handwriting improvement, and monitored progress. A sample handwriting marking guide and handwriting improvement contract are provided. (Contains 35 references.) (JDD)

Discusses two intriguing ways of explaining error in student writing--the work of Michel Foucault and the work of Roland Barthes. Describes in-class activities and essay assignments that use these perspectives to help students to reach improved understanding of error in writing. (SR)

Argues that, to deal effectively with sentence errors of basic writers, it is crucial to distinguish between what should be left alone and what can be productively marked and how it should be marked. Proposes a taxonomy of four sources of errors (knowledge, dialect, process, and developmental errors) and seven ways to address them. (SR)

Errant mathematical views are widely found among teachers, their students, and authors of applied mathematics texts. Suggests classroom experimentation, both to confirm the occurrence of these errors, and to apply the appropriate corrective teaching. (Author/ASK)

Described and listed herein with concomitant sample input and output is the Fortran IV program which estimates parameters and standard errors of estimate per parameters for parameters estimated through multiple matrix sampling. The specific program is an improved and expanded version of an earlier version. (Author/BJG)

A discussion of dictionaries and their use for second language (L2) learning suggests that lack of computerized modern language corpora can adversely affect bilingual dictionaries, commonly used by L2 learners, and shows how use of such corpora has benefitted two contemporary monolingual L2 learner dictionaries (1995 editions of the Longman Dictionary of Contemporary English and Collins Cobuild English Dictionary). The 1994 edition of the Kenkyusha New College English-Japanese Dictionary and the 1995 edition of the Kenkyusha New College Japanese-English Dictionary are examined for some recent improvements and remaining linguistic deficiencies, particularly usage errors and lack of updated word frequency, collocation, grammatical, and formality information. Examination of the two monolingual dictionaries in question shows how use of natural frequency information from modern, computerized corpora influenced the selection of lexical items, definitions, examples, grammatical patterns, and pragmatics in the dictionary entries. The importance of training in dictionary use is also highlighted. Contains 18 references. (MSE)

Eighty-seven elementary students in grades four, five, and six, were administered a 30-item multiplication instrument to assess performance in computation across grade levels. An interpretation of student performance using error ratio analysis is provided and the use of this method with groups of students for instructional decision making is suggested. (Author/CR)

Offers suggestions for the college teacher with limited opportunity for individual writing conferences with non-native English-speaking students: tolerating some more complex errors; focusing on content; soliciting student ideas for correction; addressing only one or two error types; providing vocabulary choices; and highlighting correct usage. Common error patterns are noted. (MSE)

Techniques for helping college-level non-native English speaking students understand the process of editing include individual and small-group conferencing, peer editing, and follow-up on errors. Teachers should give students the pencil, have them read the draft aloud, look for patterns of both good and erroneous usage, and focus on the positive. (MSE)

Presents a human-computer interaction (HCI) conceptions model designed to help in the understanding of the cognitive processes involved when college students learn to program computers. Examines syntactic and algorithmic HCI operational errors and reviews conceptions based on natural language reasoning, independent computer reasoning, and alternative or incomplete reasoning. (Author/JMV)

To help college teachers assist students in approaching reference materials to obtain citations, basic points that students should identify within citations are specified, and useful classroom techniques and materials are suggested. Common errors in search strategies are also noted. Some suggestions are made for selection of indexes for searching. (MSE)

This book provides a comprehensive collection of 66 teaching strategies and ideas to help overcome problems with number, each linked to a specific kind of error described in the related manual. Most of these strategies are classroom-ready and easily implemented. Some are notes for the teacher to read and then plan activities accordingly, and many are activities that can be photocopied for students to use. An index of these notes and activities cross-referenced via strategy number to each error category is given in Appendix 2. Appendix 1 provides reproducible student diagnostic outlines. Topics covered include number systems, arithmetic, calculators, order of operations, decimals, and fractions. (MKR)

This manual is a dictionary of some 150 errors made by students in their work in mathematics. A precise definition and examples are given for each of these errors and these, combined with a description of common causes of the error, form a background for diagnosis of student problems with arithmetic. Teaching strategies and ideas, each linked to a specific error, are also suggested. Chapter topics include: (1) causes of student problems in mathematics, (2) advice about reteaching, (3) how to use Stop! Look and Lesson, (4) complete list of Stop! Look and Lesson errors, (5) problems with the number system, (6) problems with algorithms, and (7) problems with fractions. Contains 144 references. (MKR)

The guide to "false friends," or false cognates, in German and English is designed such that it can be used as either an instructional tool or a reference guide. An introductory section defines false friends and discusses different types, and provides a set of symbols for distinguishing them. The first major section lists, alphabetically in German, and contains notes on "easy" false friends. Four quizzes and their answer sheets are distributed throughout this section. The second section lists more difficult false cognates, and contains four additional quizzes and answer sheets, and two final tests with answer sheets. Appended materials include German-to-English cognate lists, categorized by difficulty level and type, a list of references, and both English and German indexes. The explanatory text is entirely in German, with some notes, sample expressions, and sentences in English. (MSE)

One technique for teaching college-level report writing consists of an essay that students use as a model for their own writing. This model, in turn, contains guidelines for composing a short essay, from title and subheadings to sentence and paragraph structure, word selection, errors to avoid, and revision. (MSE)

The second guide to "false friends," or false cognates, in German and English lists and discusses more difficult terms than the first guide. An introductory section defines false friends and discusses different types, and provides a set of symbols for distinguishing them. The first major section lists, alphabetically in German, and contains notes on "difficult" false friends. Four quizzes and their answer sheets are distributed throughout this section. The second section lists particularly difficult false cognates, including "terrible twins,""tricky over-/under-compounds,""confusibles," and pseudo- Anglicisms. A quiz and answer sheet accompany each group. Two final tests with answer sheets complete the text. Appended materials include German-to-English cognate lists, categorized by difficulty level and type, a list of references, and both English and German indexes. The explanatory text is entirely in German, with some notes, sample expressions, and sentences in English. (MSE)

A discussion of classroom research on language teaching looks at what researchers have learned so far from attempts to study what happens in the language classroom. The discussion is based on the idea that it is not the currency of instructional method used that matters most, but rather a fuller understanding of classroom interaction. The first part examines the evolution of and rationale behind classroom research in general. The second part explores some major methodological issues, beginning with determining the research approach to take and proceeding to data collection and analysis. Parts 3-5 review the findings of language classroom research since the late 1960s in three areas: errors in oral language use; the complexities of classroom interaction; and aspects of learner receptivity, including anxiety, competitiveness, motivation, and self-esteem, as they relate to language learning. Part 6 closes with ideas about exploratory teaching, in which the teacher both tries new approaches and attempts to learn from their use. A section following each chapter contains ideas for starting discussion among teachers, and suggestions for further reading. Appended materials include notes on several methods of interaction analysis, observation of communication settings, transcription conventions for classroom discourse, a substantial bibliography, and author and subject indexes. (MSE)

The articles contained in this volume on second language writing evaluation focus on the evaluation of academic English learned as a second language (ESL). Essays include: "Assessment by Misconception: Cultural Influences and Intellectual Traditions" (Brigid Ballard, John Clanchy); "Reading the World Differently: A Cross-Cultural Approach to Writing Assessment" (Charlotte S. Basham, Patricia E. Kwachka); "The Writer's Knowledge and Our Knowledge of the Writer" (Liz Hamp-Lyons); "ESL Writing Assessments: Contradictions and Resolutions" (Daniel Horowitz); "Pre-Text: Task-Related Influences on the Writer" (Liz Hamp-Lyons); "Holistic Assessment: What Goes on in the Raters' Minds?" (Caroline Vaughan); "Reconstructing 'Academic Writing Proficiency'" (Liz Hamp-Lyons); "Statistical Support for Training in ESL Composition: Rating" (Fred Davidson); "Faculty Assessment of ESL Students Literacy Skills: Implications for Writing Assessment" (Ann Johns); "Error Gravity: Faculty Response to Errors in the Written Discourse of Nonnative Speakers of English" (Roberta J. Vann, Frederick O. Lorenz, Daisy M. Meyer); "Placement of ESL/EFL Undergraduate Writers in College-Level Writing Programs" (Robert Carlisle, Eleanor McKenna); "Linguistic/Rhetorical Measures for Evaluating ESL Writing" (Ulla Connor); "Using Performative Assessment Instruments with ESL Student Writers" (Sara Kurtz Allaei, Ulla Connor); "Scoring Procedures for ESL Contexts" (Liz Hamp-Lyons); "Issues in Evaluating and Maintaining an ESL Writing Assessment Program" (Grant Henning); "Program Evaluation Procedures: Reporting the Program Publicly Within the Political Context" (Sybil B. Carlson); and "Issues and Directions in Assessing Second Language Writing in Academic Contexts" (Liz Hamp-Lyons). (MSE)

Discussed are the mathematical methods for detecting a variety of common error patterns within the bar-coded identification numbers utilized in conjunction with scanning devices. Schemes for the use of check digits are examined that ensure conditions for detecting errors of specific types, including single digit error, transposition error, twin error, phonetic error, and jump twin error. (14 references) (JJK)

Discusses problems and patterns in student journalistic writing. (HOD)

This report resulted from work with primary grade children and teachers in Kankakee, Illinois. Essays by four resource persons and two observers are included, each expressing insights and feelings in order to share ideas with resource persons for primary mathematics teaching in other schools. A main objective is to represent the ways elementary school teachers think while teaching mathematics. The essays consider: general comments on learning and working with teachers, some difficulties experienced in teaching mathematics, classroom etiquette or management, a lesson on multiplication with fractions, lessons with Cuisenaire rods, equity in mathematics education, an overview of instructional policy, an in-service teacher training project, an idea about the mode of learning school requires, a report about a lesson on numeration, developing schema when teaching place value, and suggestions for resource persons. A list of references is included. (MNS)

A study was conducted in 1976 of applicants who submitted corrections or amendments to their Student Eligibility Reports (SERs) for the Basic Educational Opportunity Grant (BEOG) Program. The objective was to review the applications corrections process and to determine factors linked to applicants' use of correction procedures. Attention was focused on: characteristics of applicants using and not using the corrections system; types of corrections submitted; types and frequency of data fields corrected; degree of change in Student Eligibility Indices associated with corrections; and significance of various processing comments in terms of the type and frequency of corrections submitted. Applicant variables included: total taxable and nontaxable income, household size, marital status, and the length of time an applicant had been in postsecondary education. It was found that almost 50 percent of all corrections came from applicants reporting incomes over $12,000 a year. Additional findings are reported, along with recommendations, including: BEOG eligibility should not be established for any application that is incomplete or problematic; any SER correction resulting in BEOG eligibility for an applicant whose initial application indicated ineligibility should not be accepted. The appendices contain detailed statistical findings presented in approximately 100 tables. (SW)

The types and ranges of errors made on applications to the Basic Educational Opportunity Grant (BEOG) program were studied, along with procedures used in recovering overpayments. The objective was to assess the scope and nature of misreporting and misuse of the BEOG program. A 1975-1976 study reviewed cases referred to the U.S. Office of Education by educational institutions. Special attention was given to the reasons for institution referrals, the prevalence of confirmed errors on Student Eligibility Reports (SER), applicant characteristics associated with SER errors, and characteristics of schools sending referrals. Another study investigated a random sample of about 6,000 applicants who were selected based on 1976-1977 applications that were believed to entail errors on Student Eligibility Reports. The "high risk" applicants were selected according to specific criteria, including inconsistencies in taxes paid and reported income on the application; household size was not equal to reported tax exemptions, and SER corrections resulted in Student Eligibility Index changes greater than 250 points. Also assessed was a formal method of identifying overpayment cases and collecting BEOG funds disbursed to ineligible applicants. Statistical findings of the studies are included. (SW)